Why the 'LIKE' operator takes so much time to run?

I have a table T with 3 columns and 3 indexes:
CREATE TABLE T
id VARCHAR2(38) NOT NULL,
fid VARCHAR2(38) NOT NULL,
val NVARCHAR2(2000) NOT NULL
ALTER TABLE T ADD (CONSTRAINT pk_t PRIMARY KEY (id,fid));
CREATE INDEX t_fid ON T(fid);
CREATE INDEX t_val ON T(val);
Then I have the following two queries which differ in only one place - the 1st one uses the '=' operator whereas the 2nd uses 'LIKE'. Both queries have the identical execution plan and return one identical row. However, the 1st query takes almost 0 second to execute, and the 2nd one takes more than 12 seconds, on a pretty beefy machine. I had played with the target text, like placing '%' here and/or there, and observed the similar timing every time.
So I am wondering what I should change to make the 'LIKE' operator run as fast as the '=' operator. I know CONTEXT/CATALOG index is a viable approach, but I am just trying to find out if there is a simpler alternative, such as a better use of the index t_val.
1) Query with '=' operator
SELECT id
FROM T
WHERE fid = '{999AE6E4-1ED9-459B-9BB0-45C913668C8C}'
AND val = '3504038055275883124';
2) Query with 'LIKE' operator
SELECT id
FROM T
WHERE fid = '{999AE6E4-1ED9-459B-9BB0-45C913668C8C}'
AND val LIKE '3504038055275883124';
Execution Plan
0 SELECT STATEMENT Optimizer=ALL_ROWS (Cost=1 Card=1 Bytes=99)
1 0 TABLE ACCESS (BY INDEX ROWID) OF 'T' (Cost=1 Card=1 Bytes=99)
2 1 INDEX (RANGE SCAN) OF 'T_VAL' (NON-UNIQUE) (Cost=4 Card=12)

I will for sure try to change the order of the PK and see whether there will be any impact to the performance.
In our application, val is much closer to a unique value than fid. In the example query, the execution plan showed that the index on val was indeed used in the execution of the query. That's why the 1st query took almost no time to return (our table T has more than 6 million rows).
I was hoping the 'LIKE' operator would utilize the t_val index effectively and provide similar performance to the '=' operator. But apparently that's not the case, or needs some tricks.

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